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POD —IDEA Center
Learning Notes
S e p t e m b e r
2 0 0 6
Michael Theall, Youngstown State University, Series Editor
IDEA Learning Objective #2:
“Learning fundamental principles, generalizations, or theories”
Walt Wager, Florida State University, [email protected]
Marilla Svinicki, University of Texas at Austin, [email protected]
Background
Ms. Jones enters the classroom and gets the
student’s attention by pushing a chair across the
front of the room. She asks the class how pushing
this chair demonstrates Newton’s third law of
motion. Shenifa raises her hand and says,
“Newton’s third law is the one about an equal and
opposite reaction. So when you push the chair,
friction is pushing back and you have to apply a
force that breaks that and other forces that are
keeping the chair from moving.” “Very good,
Shenifa,” replies Ms. Jones, “How would you
describe Newton’s third law in your own words?”
In this example, Ms. Jones is working at getting the
students to “comprehend” principles, theories and
generalizations in science. Bloom (1) describes
comprehension as a level of learning above
knowledge or recall of information. Bloom states,
“…when students are confronted with a
communication, they are expected to know what is
being communicated and to be able to make some
use of the material or ideas contained in it” (1, p.
89). Shenifa had to do more than just memorize
Newton’s laws of motion in order to answer Ms.
Jones’s two questions; she had to understand them.
To know what Bloom means by this we can look at
some specifics.
How can students show they “comprehend” a
principle, generalization or theory? Bloom (1)
describes three ways. First, they can restate the
principle, generalization or theory in their own
words, which Bloom calls translation. When asked
what is Newton’s third law of motion, the student
might answer, “It’s when two things hit each other,
they push each other equally in opposite directions.”
Bloom states that translation can take one of three
forms: translation into the student’s own words, as
we’ve just seen; translation into symbolic form e.g.,
from verbal to graphical form (inserting arrows into
a picture to depict the forces operating on the chair
in the example above); translation from one verbal
form to another, e.g., metaphor, analogy.
A second way to demonstrate understanding is
what Bloom calls interpretation. The student’s
response might be – “That’s when two things push
on each other in opposite directions, the forces are
equal in both directions, like when you roll two pool
balls at each other they hit and push on each other
in opposite directions.” Another form of
interpretation might involve the student’s recognition
that the communication is describing the operation
of a principle, like realizing that Newton’s laws
explain how it is possible for car to move forward on
a road.
A third way to demonstrate understanding is
extrapolation, which “…includes the making of
predictions based on understanding of the trends,
tendencies, or conditions described in the
communication” (1, p. 90). For example, the
communication might ask, “Why is it easier for three
people to push a car than one person?” An
acceptable answer might be that the car pushes
back with a force equal to the force of the person
pushing it, so with more people pushing, the force is
distributed among the three. While there may be
any number of acceptable responses, the answer
would have to include the following components 1)
a force, 2) an equal counter force, and 3) in the
opposite direction.
Helpful Hints
So, what teaching techniques are appropriate for
attaining these desired levels of understanding?
Gain and direct attention. Do something to focus the
learner on the learning task at hand (2, 3). In the
case of principles, the instructor might start with a
question to pique the curiosity about the principle to
be learned, and point to its application to the real
world. This foreshadows the eventual focus on
principles rather than facts. IDEA research has
found that several instructional methods related to
“stimulating student interest” are important to
engaging the learner in the principles and theories
addressed in courses (see POD-IDEA Center Note
#4 “Demonstrated the importance and significance
of the subject matter,” #8 “Stimulated students to
intellectual effort beyond that required by most
courses,” and #13 "Introduced stimulating ideas
about the subject").
Make clear how each topic fits in the course (see
POD-IDEA Note #6). In comprehension learning
tasks, the student must understand the meaning of
the component concepts, and the relationships
among them.
Recall prerequisite learning and connect to new
material. All new learning is hooked in some way
into previous learning (2, 3). Comprehension
involves bringing to mind previously learned
knowledge related to the new learning. In this case
it is likely that the student has encountered an
explanation of Newton’s first and second laws. So
they are familiar with the concepts of inertia, mass,
force, acceleration. If during instruction these laws
are tied together such that an understanding of one
can be used to support understanding of the next,
the chances are good that the students will learn
the similarities and differences among them, and
will be able to differentiate the examples that
represent each of the theories or principles.
Theories of how concepts like these are learned
suggest that, after reminding students of where they
might have encountered this concept before (either
personally or in a previous class), the instructor
would give a good, clear definition of the concept
followed by what is called a “paradigmatic
example,” which is simply the example that most
people would think of if you asked for an example of
the concept. For example, in the case of Newton’s
laws, the example of rolling a ball along a surface is
the simplest example that would come to mind for
most people. The instructor could even use bowling
or soccer as a more concrete example that most
students would recognize. (This example later
serves as a benchmark against which to check
every other example they think of, so it pays to think
it through thoroughly.) Then the instructor or the
students generate other examples of the principle.
Seeing or even categorizing positive and negative
instances (non-examples) of the concept helps the
students to clarify their understanding. The
instructor can illustrate different relationships or
characteristics of the concept by moving on to more
complex or related examples, for example, using
the example of how different strengths of the bowler
would cause the ball to roll faster or slower. In fact,
the instructor could even invite the students to
suggest other scenarios and what they might say
about the concept.
Use the three modes of understanding (translation,
interpretation, and extrapolation) in the examples
given during instruction. The use of these three
modes of understanding would represent learning
guidance in the form of elaboration with a variety of
examples of the concepts or principles being
learned. Translation can be accomplished by having
the students state the principles in their own terms;
there could even be a contest to see who comes up
with the best alternative statement of the principle
or theory. For interpretation, the students could be
asked to demonstrate the principle or draw a graph
of it. For extrapolation, the teacher might
demonstrate the interaction of two moving objects
and ask the students what they think will happen if
some variable changes. The teacher might explore
the related concepts and principles at the same
time, so the students might see how they relate to
each other.
Incorporate practice and feedback. One important
component of learning at this level is practice and
feedback. The principle just learned should become
the foundation for learning future principles.
Furthermore, the more the principle is used in future
activities, the better and stronger the neural
connections (4), and the easier it will be to recall
and use. Unfortunately, research in the area of
transfer has shown that many students fail to
recognize that previously learned skills can be
transferred to a new task situation unless they are
prompted to do so (5). However, the more often
this type of spaced practice occurs, the higher the
probability that learners will develop an orientation
for transfer (6).
The students would get practice in the elaboration
activity suggested above, and the results could be
used by the teacher to reinforce correct
understanding and remediate misunderstanding.
Practice and feedback can be accomplished in
many different ways, from collaborative activity to
computerized tutorials and quizzes. Especially
helpful are engaging activities where the students
can practice putting things into their own words,
giving examples of the principles or theories,
illustrating with graphics or models, and/or, given a
set of conditions, setting up a demonstration. This
practice allows students to get feedback on their
understanding.
The importance of feedback can’t be overstated.
Students value feedback, as it confirms their
understanding or misunderstanding while learning is
still taking place. It’s easier to learn things the right
way the first time than try to unlearn and relearn it
later.
Model intellectual skills. Consider employing the
“cognitive apprenticeship” model. In this model the
instructor acts as a master model to illustrate the
intellectual skill being learned and then coaches the
students as they practice solving real problems
using those illustrated strategies (7).
Assessment Issues
Assessment of comprehension tasks follows the
same pattern as the behaviors practiced in
instruction. The student can be asked to identify
relevant theories or principles when given a
scenario, or be asked to translate, interpret or
extrapolate a particular principle within a range of
conditions. However, assessment of
comprehension should stay within the parameters
described in the statement of instructional
outcomes. That is, if learning is at the
comprehension level, assessment should not test
application or evaluation of the principles or
concepts.
Finally, instruction should include opportunities for
lots of practice spaced out across the learning.
Spaced practice is periodic use of the principles in
dialog and other learning activities. Knowledge that
is not practiced or used to support new knowledge
quickly decays, and becomes inert knowledge.
Reminding students in successive class periods of
what they learned before and having them do
something with that information will keep it fresh
and eventually more solidly stored in long term
memory. This is the principle behind a spiral
curriculum, in which the instruction returns to earlier
principles but in more complex situations. An
example would be moving from comprehension to
application of a principle in a subsequent class
period.
Comprehension of fundamental principles,
generalizations, and theories is generally taught as
a prerequisite for application level learning, where
students are expected to demonstrate
understanding by applying the knowledge they just
learned to new situations they haven’t encountered
before. Instruction that teaches comprehension
level learning should be followed as soon as
possible with application level activities. Application
level learning strengthens the students’ ability to
recall the previously learned knowledge.
Applications are potentially more meaningful and
motivating to students, especially if they have a
manipulative and or emotional component, because
they reinforce the conceptual understanding
associated with comprehension. Comprehension of
fundamental principles, generalizations and theories
can be an exciting and motivating part of learning,
and it facilitates the students’ future application of
knowledge. Because of this, it is worth the time and
effort to teach it.
References and Resources
(1) Bloom, B. S. (Ed.). (1956). Taxonomy of
educational objectives: The classification of
educational goals handbook I: Cognitive
domain. New York: David McKay Company, Inc.
(2) Gagne, R. M. (1977). The conditions of learning,
3rd Ed. NY: Holt Rinehart & Winston
(3) Gagne, R. M., Wager, W. W., Golas, K. C., &
Keller, J. M. (2005). Principles of Instructional
Design, 5th Ed. Stamford, CT:
Wadsworth/Thomson.
(4) Zull, J. E. (2002). The art of changing the brain.
Sterling, VA: Stylus Publishing
(5) Gick, M., & Holyoak, K. (1980) Analogical
problem solving. Cognitive Psychology, 12, 306355.
(6) Bransford, J., Brown, A., & Cocking, R. (Eds.)
(1999). How people learn: Brain, mind,
experience and school. Washington, DC:
National Academy Press.
(7) Collins, A. (1991). Cognitive apprenticeship and
instructional technology. In L. Idol & B.F. Jones
(Eds.), Educational values and cognitive
instruction: Implications for reform (pp. 121138). Hillsdale, NJ: Lawrence Erlbaum
Associates, Inc.
Related POD-IDEA Center Notes
Additional Resources
IDEA Item #4 “Demonstrated the importance and
significance of the subject matter,” Nancy McClure
IDEA Paper No. 24: Improving Instructors' Speaking
Skills, Goulden
IDEA Item #6 “Made it clear how each topic fit into
the course," Michael Theall
IDEA Paper No. 41: Student Goal Orientation,
Motivation, and Learning, Svinicki
IDEA Item #8 “Stimulated students to intellectual
effort beyond that required by most courses,” Nancy
McClure
IDEA Item #12 “Gave tests, projects, etc. that
covered the most important parts of the course,”
Barbara E. Walvoord
IDEA Item #13 "Introduced stimulating ideas about
the subject," Michael Theall
IDEA Item #15 “Inspired students to set and
achieve goals which really challenged them,” Todd
Zakrajsek
©2006 The IDEA Center
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